Banach空间二阶脉冲微分方程三点边值问题正解存在性

Existence of Positive Solution of Three-Point Boundary Value Problems for Second-Order Impulsive Differential Equation in Banach Space

关于非线性脉冲微分方程边值问题解、正解以及多个正解存在性的讨论在已有文献中涉及的方法有很多。包括上下解方法、不动点指数理论等.在Banach空间中利用严格集压缩算子范数形式的锥拉伸与锥压缩不动点定理讨论一类非线性脉冲微分方程三点边值问题的特殊情况,即η∈(t_m,1]正解和多个正解的存在性.并运用该定理考察了一个无穷维脉冲微分方程三点边值问题正解的存在性.

There were many methods were used in other papers to discuss the existence of solutions, positive solutions and multiple positive solutions of boundary value problem for nonlinear impulsive differential equation, such as the method of upper and lower solution, fixed point index theory. The fixed point theorem of cone is used to study the existence of multiple positive solutions to three-point boundary value problem as a case in particular to the nonlinear impulsive equation, i. e. , η∈（ tm, 1] in Banach space. And an example is given to show the application of main result.